Florian Frick

About

Florian Frick is an Associate Professor in the Department of Mathematical Sciences at Carnegie Mellon University. Prior to joining CMU, he was an H.C. Wang Assistant Professor at Cornell University and completed his Ph.D. at TU Berlin. He has held visiting positions at MSRI in Berkeley during the Fall semester of 2017 and at Freie Universität Berlin during the 2021/22 academic year. His research develops geometric and topological methods to solve problems of both geometric nature and those beyond, by "geometrizing" problems that benefit from topological techniques, which are particularly effective in tracking global phenomena. Among the topological methods he develops are existence and nonexistence results for equivariant maps and embeddings of topological spaces, as well as fixed-point theorems. Beyond algebraic and geometric topology, he applies these tools to diverse problems including chromatic numbers of hypergraphs in combinatorics, fair division results in game theory and convex geometry, the large-scale structure of point sets in computational topology, and polytope theory. Within geometric topology, his work includes the theory of embeddings, manifold triangulations, inscribability problems, and metric geometry.

Research topics

• Computer Security
• Computer Science
• Distributed computing
• Computer network
• Engineering
• Embedded system

Selected publications

• Youden's demon is Sylvester's problem

  Mathematika · 2025-02-18 · 2 citations

  articleOpen access1st authorCorresponding

  Abstract If four people with Gaussian‐distributed heights stand at Gaussian positions on the plane, the probability that there are exactly two people whose height is above the average of the four is exactly the same as the probability that they stand in convex position; both probabilities are . We show that this is a special case of a more general phenomenon: The problem of determining the position of the mean among the order statistics of Gaussian random points on the real line (Youden's demon…

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• Hausdorff vs Gromov–Hausdorff Distances

  Discrete & Computational Geometry · 2025-02-19 · 1 citations

  article
  PublisherDOI

• Youden's Demon is Sylvester's Problem

  arXiv (Cornell University) · 2024-07-02 · 1 citations

  preprintOpen access1st authorCorresponding

  If four people with Gaussian-distributed heights stand at Gaussian positions on the plane, the probability that there are exactly two people whose height is above the average of the four is exactly the same as the probability that they stand in convex position; both probabilities are $\frac 6 π\arcsin\left(\frac{1}{3}\right)\approx .649$. We show that this is a special case of a more general phenomenon: The problem of determining the position of the mean among the order statistics of Gaussian ra…

  PublisherOA PDFDOI

• Vertex numbers of simplicial complexes with free abelian fundamental group

  Ars Mathematica Contemporanea · 2023-09-26 · 1 citations

  articleOpen access1st authorCorresponding

  We show that the minimum number of vertices of a simplicial complex with fundamental group ℤn is at most O(n) and at least Ω(n3/4). For the upper bound, we use a result on orthogonal 1-factorizations of K2n. For the lower bound, we use a fractional Sylvester–Gallai result. This application of extremal results in discrete geometry seems to be new. We also prove that any group presentation ⟨S|R⟩ ≅ ℤn whose relations are of the form gahbic for g, h, i ∈ S has at least Ω(n3/2) generators.

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• Topological methods in zero-sum Ramsey theory

  arXiv (Cornell University) · 2023-10-25 · 1 citations

  preprintOpen access1st authorCorresponding

  A cornerstone result of Erd\H os, Ginzburg, and Ziv (EGZ) states that any sequence of $2n-1$ elements in $\mathbb{Z}/n$ contains a zero-sum subsequence of length $n$. While algebraic techniques have predominated in deriving many deep generalizations of this theorem over the past sixty years, here we introduce topological approaches to zero-sum problems which have proven fruitful in other combinatorial contexts. Our main result (1) is a topological criterion for determining when any $\mathbb{Z}/n…

  PublisherOA PDFDOI

Recent grants

• Topological Methods for Discrete Problems

  NSF · $180k · 2019–2023

Frequent coauthors

• Zoe Wellner

  21 shared

• Ling Hei Tsang

  The Ohio State University

  19 shared

• Megumi Asada

  Williams College

  19 shared

• Maxwell Polevy

  Cornell University

  19 shared

• David Stoner

  Stanford University

  19 shared

• Anne Shiu

  Texas A&M University

  17 shared

• Aaron Chen

  17 shared

• Vivek Pisharody

  17 shared

Education

• Ph.D.

  Technische Universität Berlin and Berlin Mathematical School

Awards & honors

• NSF CAREER Award

Similar researchers at Carnegie Mellon University

• Alan Friezeh-74
• Michael Youngh-57
• David Kinderlehrerh-45